How to set Output path correctly for a Single Image render?
If you are Rendering single image Image using the Render> Render Image menu or f12, Blender will not save the image automatically.



You have to save it manually, by clicking Image option located at the left of Render Result dropdown and select Save as (or press Shift+s while in the image editor).



A new window will open where you can choose where to save the file.

If you want to save the image automatically you can render as animation.

Set the frame range to a single frame.



Then render using the Render animation option or F12. 

Note that 2.8 has different panel for output.

Dimensions and frame range can be set there as well.